Once you start the “Boo-Boo Roverdrive” mission and step outside of Sasquatch & Friends, you can begin gathering Badges, which are the currency used to unlock and upgrade Overdrives. You will be informed of this by the magical tutorial voice inside your head, which sounds like sarcasm but is exactly what happens.
There are twelve different kinds of Badges: Single-Shot, Deployable, Automatic, Melee, Traps, Fizzco Killing, OD Killing, Scab Killing, Grind, Wall Run, Bounce, and Pole Swing. Each is tied to a specific type of combat—fighting with a particular kind of weapon, or against a particular type of enemy—or a method of traversal.
As you perform Badge-related activities, you gradually fill up a meter attached to it, which you can see on the Overdrives page in the Character screen. When that meter’s full, you earn a Badge, the meter empties, and the cycle repeats itself. You can then spend your earned Badges to unlock or upgrade Overdrives.
The Badges are an incentive to change your playstyle from time to time, by using different weapons and traversal abilities or taking on new challenges. There aren’t any real ways to speed up the process, short of deliberately pursuing a single activity for long periods of time. Fortunately, since you earn credit towards a Badge for doing anything other than running or standing still, you should get most of the Badges you need simply by playing the game.
There’s one exception, however, and that’s the Pole Swing Badge. There are poles to swing from all over the city and you should get a couple of Pole Swing Badges simply by collecting Toilet Paper, but it’s not as ubiquitous a method of travel as grinding, bouncing, or even running along walls. As a result, you often have fewer Pole Swing Badges than any other kind, which can slow down the rate at which you can unlock various Style Overdrives.
As you move around Sunset City, keep an eye out for poles you can swing from here and there, just to extend your traversal combo and earn the occasional extra Badge. If all else fails, head to the city’s southeast side and the Stand Your Ground pier, where there are multiple poles to swing from located on the docks. (You also visit this area during the “Fizzco: The Untold Story” quests.) You can swing from one pole to another out here more or less indefinitely and farm Pole Swing Badges in relative peace.
Overdrives can be upgraded as far as level 4 by spending more Badges on them, increasing their benefits and, if present, drawbacks.